858 Questions 1. O (iii) (iv) 11. O 2. O (i) (ii) 12. O 3. O (i) 13. (ii) 14. O 5. O 6. O 15. O O (i) (ii)

Transcription

1 858 Chpte 30 Souces of the Mgnetic Field Questions denotes nswe vilble in Student Solutions Mnul/Stud Guide; O denotes objective question 1. O Wht cetes mgnetic field? Choose eve coect nswe. () sttion object with electic chge (b) moving object with electic chge (c) sttion conducto cing electic cuent (d) diffeence in electic potentil (e) n electic esisto. Note: n Chpte 34, we will see tht chnging electic field lso cetes mgnetic field. 2. O A long, veticl, metllic wie cies downwd electic cuent. (i) Wht is the diection of the mgnetic field it cetes t point 2 cm hoiontll est of the cente of the wie? () noth (b) south (c) est (d) west (e) up (f) down (ii) Wht would be the diection of the field if the cuent consisted of positive chges moving downwd, insted of electons moving upwd? Choose fom the sme possibilities. 3. O Suppose ou e fcing tll mkeup mio on veticl wll. Fluoescent tubes fming the mio c clockwise electic cuent. (i) Wht is the diection of the mgnetic field ceted b tht cuent t point slightl to the ight of the cente of the mio? () up (b) down (c) left (d) ight (e) hoiontll towd ou (f) w fom ou (ii) Wht is the diection of the field the cuent cetes t point on the wll outside the fme to the ight? Choose fom the sme possibilities. 4. Eplin wh two pllel wies cing cuents in opposite diections epel ech othe. 5. O n Active Figue 30.8, ssume 1 2 A nd 2 6 A. Wht is the eltionship between the mgnitude F 1 of the foce eeted on wie 1 nd the mgnitude F 2 of the foce eeted on wie 2? () F 1 6F 2 (b) F 1 3F 2 (c) F 1 F 2 (d) F 1 F 2 /3 (e) F 1 F 2 /6 6. O Answe ech question es o no. () s it possible fo ech of thee sttion chged pticles to eet foce of ttction on the othe two? (b) s it possible fo ech of thee sttion chged pticles to epel both of the othe pticles? (c) s it possible fo ech of thee cuentcing metl wies to ttct the othe two? (d) s it possible fo ech of thee cuent-cing metl wies to epel both of the othe wies? Andé-Mie Ampèe s epeiments on electomgnetism e models of logicl pecision nd included obsevtion of the phenomen efeed to in this question. 7. s Ampèe s lw vlid fo ll closed pths suounding conducto? Wh is it not useful fo clculting B S fo ll such pths? 8. Compe Ampèe s lw with the Biot Svt lw. Which is moe genell useful fo clculting B S fo cuentcing conducto? 9. A hollow coppe tube cies cuent long its length. Wh is B S 0 inside the tube? s B S noneo outside the tube? 10. O (i) Wht hppens to the mgnitude of the mgnetic field inside long solenoid if the cuent is doubled? () t becomes 4 times lge. (b) t becomes twice s lge. (c) t is unchnged. (d) t becomes one-hlf s lge. (e) t becomes one-fouth s lge. (ii) Wht hppens to the field if insted the length of the solenoid is doubled, with the numbe of tuns emining the sme? Choose fom the sme possibilities. (iii) Wht hppens to the field if the numbe of tuns is doubled, with the length emining the sme? Choose fom the sme possibilities. (iv) Wht hppens to the field if the dius is doubled? Choose fom the sme possibilities. 11. O A long solenoid with closel spced tuns cies electic cuent. Does ech tun of wie eet () n ttctive foce on the net djcent tun, (b) epulsive foce on the net djcent tun, (c) eo foce on the net djcent tun, o (d) eithe n ttctive o epulsive foce on the net tun, depending on the diection of cuent in the solenoid? 12. O A unifom mgnetic field is diected long the is. Fo wht oienttion of flt, ectngul coil is the flu though the ectngle mimum? () t is mimum in the plne. (b) t is mimum in the plne. (c) t is mimum in the plne. (d) The flu hs the sme noneo vlue fo ll these oienttions. (e) The flu is eo in ll cses. 13. The quntit B S d S s in Ampèe s lw is clled mgnetic cicultion. Active Figue nd Figue show pths ound which the mgnetic cicultion ws evluted. Ech of these pths encloses n e. Wht is the mgnetic flu though ech e? Eplin ou nswe. 14. O () Two sttion chged pticles eet foces of ttction on ech othe. One of the pticles hs negtive chge. s the othe positive o negtive? (b) s the net electic field t point hlfw between the pticles lge, smlle, o the sme in mgnitude s the field due to one chge b itself? (c) Two stight, veticl, cuent-cing wies eet foces of ttction on ech othe. One of them cies downwd cuent. Does the othe wie c upwd o downwd cuent? (d) s the net mgnetic field t point hlfw between the wies lge, smlle, o the sme in mgnitude s the field due to one wie b itself? 15. O nk the mgnitudes of the following mgnetic fields fom the lgest to the smllest, noting n cses of equlit. () the field 2 cm w fom long, stight wie cing cuent of 3 A (b) the field t the cente of flt, compct, cicul coil, 2 cm in dius, with 10 tuns, cing cuent of 0.3 A (c) the field t the cente of solenoid 2 cm in dius nd 200 cm long, with tuns, cing cuent of 0.3 A (d) the field t the cente of long, stight metl b, 2 cm in dius, cing cuent of 300 A (e) field of 1 mt 16. One pole of mgnet ttcts nil. Will the othe pole of the mgnet ttct the nil? Eplin. Eplin how mgnet sticks to efigeto doo. 17. A mgnet ttcts piece of ion. The ion cn then ttct nothe piece of ion. On the bsis of domin lignment, eplin wht hppens in ech piece of ion. 18. Wh does hitting mgnet with hmme cuse the mgnetism to be educed? 19. Which w would compss point if ou wee t the noth mgnetic pole of the Eth?

2 oblems Figue Q30.20 shows fou pemnent mgnets, ech hving hole though its cente. Notice tht the blue nd ellow mgnets e levitted bove the ed ones. () How does this levittion occu? (b) Wht pupose do the ods seve? (c) Wht cn ou s bout the poles of the mgnets fom this obsevtion? (d) f the uppe mgnet wee inveted, wht do ou suppose would hppen? Thomson Lening/Chles D. Wintes Figue Q30.20 oblems The oblems fom this chpte m be ssigned online in WebAssign. Sign in t nd go to ThomsonNOW to ssess ou undestnding of this chpte s topics with dditionl quiing nd conceptul questions. 1, 2, 3 denotes stightfowd, intemedite, chllenging; denotes full solution vilble in Student Solutions Mnul/Stud Guide; denotes coched solution with hints vilble t denotes developing smbolic esoning; denotes sking fo qulittive esoning; denotes compute useful in solving poblem Section 30.1 The Biot Svt Lw 1. n Niels Boh s 1913 model of the hdogen tom, n electon cicles the poton t distnce of m with speed of m/s. Compute the mgnitude of the mgnetic field this motion poduces t the loction of the poton. 2. Clculte the mgnitude of the mgnetic field t point 100 cm fom long, thin conducto cing cuent of 1.00 A. 3. () A conducto in the shpe of sque loop of edge length m cies cuent 10.0 A s shown in Figue Clculte the mgnitude nd diection of the mgnetic field t the cente of the sque. (b) Wht f? f this conducto is fomed into single cicul tun nd cies the sme cuent, wht is the vlue of the mgnetic field t the cente? Figue A conducto consists of cicul loop of dius nd two stight, long sections s shown in Figue The wie lies in the plne of the ppe nd cies cuent. Find n epession fo the vecto mgnetic field t the cente of the loop. 5. Detemine the mgnetic field t point locted distnce fom the cone of n infinitel long wie bent t ight ngle s shown in Figue The wie cies sted cuent. Figue Conside flt, cicul cuent loop of dius cing cuent. Choose the is to be long the is of the loop, with the oigin t the cente of the loop. lot gph of the tio of the mgnitude of the mgnetic field t coodinte to tht t the oigin, fo 0 to 5. t m be useful to use pogmmble clculto o compute to solve this poblem. 7. Two long, stight, pllel wies c cuents tht e diected pependicul to the pge s shown in Figue Wie 1 cies cuent 1 into the pge (in the diection) nd psses though the is t. Wie 2 psses though the is t 2 nd cies n unknown cuent 2. The totl mgnetic field t the oigin due to the cuent-cing wies hs the mgnitude 2m 0 1 /(2p). The cuent 2 cn hve eithe of two possible vlues. () Find the vlue of 2 with the smlle mgnitude, stting it in tems of 1 nd giving its diection. (b) Find the othe possible vlue of Figue 30.7 Figue A long, stight wie cies cuent. A ight-ngle bend is mde in the middle of the wie. The bend foms n c 2 = intemedite; 3 = chllenging; = SSM/SG; = ThomsonNOW; = smbolic esoning; = qulittive esoning

3 860 Chpte 30 Souces of the Mgnetic Field of cicle of dius s shown in Figue Detemine the mgnetic field t the cente of the c. Figue One long wie cies cuent 30.0 A to the left long the is. A second long wie cies cuent 50.0 A to the ight long the line ( m, 0). () Whee in the plne of the two wies is the totl mgnetic field equl to eo? (b) A pticle with chge of 2.00 mc is moving with velocit of 150 î Mm/s long the line ( m, 0). Clculte the vecto mgnetic foce cting on the pticle. (c) Wht f? A unifom electic field is pplied to llow this pticle to pss though this egion undeflected. Clculte the equied vecto electic field. 10. A cuent pth shped s shown in Figue poduces mgnetic field t, the cente of the c. f the c subtends n ngle of 30.0 nd the dius of the c is m, wht e the mgnitude nd diection of the field poduced t if the cuent is 3.00 A? 30.0 Figue Thee long, pllel conductos c cuents of 2.00 A. Figue is n end view of the conductos, with ech cuent coming out of the pge. Tking 1.00 cm, detemine the mgnitude nd diection of the mgnetic field t points A, B, nd C. ppoimtion to model the electon s moving in unifom field? Eplin ou nswe. (c) f it does not collide with n obstcles, how mn evolutions will the electon complete duing the 60.0-ms dution of the lightning stoke? 13. A wie cing cuent is bent into the shpe of n equiltel tingle of side L. () Find the mgnitude of the mgnetic field t the cente of the tingle. (b) At point hlfw between the cente nd n vete, is the field stonge o weke thn t the cente? Give qulittive gument fo ou nswe. 14. Detemine the mgnetic field (in tems of,, nd d) t the oigin due to the cuent loop in Figue d O + Figue Two long, pllel conductos c cuents A nd A, both diected into the pge in Figue Detemine the mgnitude nd diection of the esultnt mgnetic field t cm cm 12.0 cm 2 Figue A B C Figue The ide tht mgnetic field cn hve thepeutic vlue hs been ound fo centuies. A e-eth mgnet sold to elieve joint pin is disk 1.20 mm thick nd 3.50 mm in dimete. ts cicul flt fces e its noth nd south poles. Assume it is ccutel modeled s mgnetic dipole. Also ssume Eqution descibes the mgnetic field it poduces t ll points long its is. The field is stongest, with the vlue 40.0 mt, t the cente of ech flt fce. At wht distnce fom the sufce is the mgnitude of the mgnetic field like tht of the Eth, with vlue of 50.0 mt? 12. n long, stight, veticl lightning stoke, electons move downwd nd positive ions move upwd, to constitute cuent of mgnitude 20.0 ka. At loction 50.0 m est of the middle of the stoke, fee electon difts though the i towd the west with speed of 300 m/s. () Find the vecto foce the lightning stoke eets on the electon. Mke sketch showing the vious vectos involved. gnoe the effect of the Eth s mgnetic field. (b) Find the dius of the electon s pth. s it good Section 30.2 The Mgnetic Foce Between Two llel Conductos 17. n Figue 30.17, the cuent in the long, stight wie is A nd the wie lies in the plne of the ectngul loop, which cies the cuent A. The dimensions e c m, m, nd m. Find the mgnitude nd diection of the net foce eeted on the loop b the mgnetic field ceted b the wie. 2 = intemedite; 3 = chllenging; = SSM/SG; = ThomsonNOW; = smbolic esoning; = qulittive esoning

4 oblems c 18. Two long, pllel conductos, septed b 10.0 cm, c cuents in the sme diection. The fist wie cies cuent A, nd the second cies A. () Wht is the mgnitude of the mgnetic field ceted b 1 t the loction of 2? (b) Wht is the foce pe unit length eeted b 1 on 2? (c) Wht is the mgnitude of the mgnetic field ceted b 2 t the loction of 1? (d) Wht is the foce pe length eeted b 2 on 1? 19. Two long, pllel wies e ttcted to ech othe b foce pe unit length of 320 mn/m when the e septed b veticl distnce of m. The cuent in the uppe wie is 20.0 A to the ight. Detemine the loction of the line in the plne of the two wies long which the totl mgnetic field is eo. 20. Thee long wies (wie 1, wie 2, nd wie 3) hng veticll. The distnce between wie 1 nd wie 2 is 20.0 cm. On the left, wie 1 cies n upwd cuent of 1.50 A. To the ight, wie 2 cies downwd cuent of 4.00 A. Wie 3 is to be locted such tht when it cies cetin cuent, ech wie epeiences no net foce. () s this sitution possible? s it possible in moe thn one w? Descibe (b) the position of wie 3 nd (c) the mgnitude nd diection of the cuent in wie The unit of mgnetic flu is nmed fo Wilhelm Webe. A pcticl-sie unit of mgnetic field is nmed fo Johnn Kl Fiedich Guss. Both wee scientists t Göttingen, Gemn. Along with thei individul ccomplishments, togethe the built telegph in t consisted of btte nd switch, t one end of tnsmission line 3 km long, opeting n electomgnet t the othe end. (Andé Ampèe suggested electicl signling in 1821; Smuel Mose built telegph line between Bltimoe nd Wshington, D.C., in 1844.) Suppose Webe nd Guss s tnsmission line ws s digmmed in Figue Two long, pllel wies, ech hving mss pe unit length of 40.0 g/m, e suppoted in hoiontl plne b stings 6.00 cm long. When both wies c the sme cuent, the wies epel ech othe so tht the ngle u between the suppoting stings is () Ae the cuents in the sme diection o in opposite diec- 2 Figue tions? (b) Find the mgnitude of the cuent. (c) f this pptus wee tken to Ms, would the cuent equied to septe the wies b 16 be lge o smlle thn on Eth? Wh? 22. Two pllel coppe conductos e ech m long. The c 10.0-A cuents in opposite diections. () Wht cente-to-cente seption must the conductos hve if the e to epel ech othe with foce of 1.00 N? (b) s this sitution phsicll possible? Eplin. Section 30.3 Ampèe s Lw 23. Fou long, pllel conductos c equl cuents of 5.00 A. Figue is n end view of the conductos. The cuent diection is into the pge t points A nd B (indicted b the cosses) nd out of the pge t C nd D (indicted b the dots). Clculte the mgnitude nd diection of the mgnetic field t point, locted t the cente of the sque of edge length m. A B C D m Figue m 24. A long, stight wie lies on hoiontl tble nd cies cuent of 1.20 ma. n vcuum, poton moves pllel to the wie (opposite the cuent) with constnt speed of m/s t distnce d bove the wie. Detemine the vlue of d. You m ignoe the mgnetic field due to the Eth. 25. Figue is coss-sectionl view of coil cble. The cente conducto is suounded b ubbe le, which is suounded b n oute conducto, which is suounded b nothe ubbe le. n pticul ppliction, the cuent in the inne conducto is 1.00 A out of the pge nd the cuent in the oute conducto is 3.00 A into the pge. Detemine the mgnitude nd diection of the mgnetic field t points nd b A 3.00 A b cm u 16.0 Figue mm 1 mm 1 mm Figue The mgnetic field 40.0 cm w fom long,stight wie cing cuent 2.00 A is 1.00 mt. () At wht distnce is it mt? (b) Wht f? At one instnt, the two conductos in long household etension cod c equl 2.00-A cuents in opposite diections. The two wies e 3.00 mm pt. Find the mgnetic field 40.0 cm w 2 = intemedite; 3 = chllenging; = SSM/SG; = ThomsonNOW; = smbolic esoning; = qulittive esoning

5 862 Chpte 30 Souces of the Mgnetic Field fom the middle of the stight cod, in the plne of the two wies. (c) At wht distnce is it one-tenth s lge? (d) The cente wie in coil cble cies cuent 2.00 A in one diection, nd the sheth ound it cies cuent 2.00 A in the opposite diection. Wht mgnetic field does the cble cete t points outside? 27. A pcked bundle of 100 long, stight, insulted wies foms clinde of dius cm. () f ech wie cies 2.00 A, wht e the mgnitude nd diection of the mgnetic foce pe unit length cting on wie locted cm fom the cente of the bundle? (b) Wht f? Would wie on the oute edge of the bundle epeience foce gete o smlle thn the vlue clculted in pt ()? Give qulittive gument fo ou nswe. 28. The mgnetic coils of tokmk fusion ecto e in the shpe of tooid hving n inne dius of m nd n oute dius of 1.30 m. The tooid hs 900 tuns of lge-dimete wie, ech of which cies cuent of 14.0 ka. Find the mgnitude of the mgnetic field inside the tooid long () the inne dius nd (b) the oute dius. 29. Conside column of electic cuent pssing though plsm (ionied gs). Filments of cuent within the column e mgneticll ttcted to one nothe. The cn cowd togethe to ield ve get cuent densit nd ve stong mgnetic field in smll egion. Sometimes the cuent cn be cut off momentil b this pinch effect. (n metllic wie, pinch effect is not impotnt becuse the cuent-cing electons epel one nothe with electic foces.) The pinch effect cn be demonstted b mking n empt luminum cn c lge cuent pllel to its is. Let epesent the dius of the cn nd the upwd cuent, unifoml distibuted ove its cuved wll. Detemine the mgnetic field () just inside the wll nd (b) just outside. (c) Detemine the pessue on the wll. 30. Niobium metl becomes supeconducto when cooled below 9 K. ts supeconductivit is destoed when the sufce mgnetic field eceeds T. Detemine the mimum cuent 2.00-mm-dimete niobium wie cn c nd emin supeconducting, in the bsence of n etenl mgnetic field. 31. A long, clindicl conducto of dius cies cuent s shown in Figue The cuent densit J, howeve, is not unifom ove the coss section of the conducto but is function of the dius ccoding to J b, whee b is constnt. Find n epession fo the mgnetic field mgnitude B () t distnce 1 nd (b) t distnce 2, mesued fom the is. 2 1 Figue n Figue 30.32, both cuents in the infinitel long wies e 8.00 A in the negtive diection. The wies e septed b the distnce cm. () Sketch the mgnetic field ptten in the plne. (b) Wht is the vlue of the mgnetic field t the oigin? At ( 0, S )? (c) Find the mgnetic field t points long the is s function of. (d) At wht distnce d long the positive is is the mgnetic field mimum? (e) Wht is this mimum vlue? Figue An infinite sheet of cuent ling in the plne cies sufce cuent of line densit J s. The cuent is in the diection, nd J s epesents the cuent pe unit length mesued long the is. Figue is n edge view of the sheet. ove tht the mgnetic field ne the sheet is pllel to the sheet nd pependicul to the cuent diection, with mgnitude m 0 J s /2. Suggestion: Use Ampèe s lw nd evlute the line integl fo ectngul pth ound the sheet, epesented b the dshed line in Figue J s (out of ppe) Figue Section 30.4 The Mgnetic Field of Solenoid 34. You e given cetin volume of coppe fom which ou cn mke coppe wie. To insulte the wie, ou cn hve s much enmel s ou like. You will use the wie to mke tightl wound solenoid 20 cm long hving the getest possible mgnetic field t the cente nd using powe suppl tht cn delive cuent of 5 A. The solenoid cn be wpped with wie in one o moe les. () Should ou mke the wie long nd thin o shote nd thick? Eplin. (b) Should ou mke the solenoid dius smll o lge? Eplin. 35. Wht cuent is equied in the windings of long solenoid tht hs tuns unifoml distibuted ove length of m to poduce t the cente of the solenoid mgnetic field of mgnitude T? 36. Conside solenoid of length nd dius, contining N closel spced tuns nd cing sted cuent. () n tems of these pmetes, find the mgnetic field t point long the is s function of distnce fom the end of the solenoid. (b) Show tht s becomes ve long, B ppoches m 0 N/2 t ech end of the solenoid. 2 = intemedite; 3 = chllenging; = SSM/SG; = ThomsonNOW; = smbolic esoning; = qulittive esoning

6 oblems A single-tun sque loop of wie, 2.00 cm on ech edge, cies clockwise cuent of A. The loop is inside solenoid, with the plne of the loop pependicul to the mgnetic field of the solenoid. The solenoid hs 30 tuns/cm nd cies clockwise cuent of 15.0 A. Find the foce on ech side of the loop nd the toque cting on the loop. 38. A solenoid 10.0 cm in dimete nd 75.0 cm long is mde fom coppe wie of dimete cm, with ve thin insultion. The wie is wound onto cdbod tube in single le, with djcent tuns touching ech othe. Wht powe must be deliveed to the solenoid if it is to poduce field of 8.00 mt t its cente? Section 30.5 Guss s Lw in Mgnetism 39. A cube of edge length 2.50 cm is positioned s shown in Figue A unifom mgnetic field given b B S 15 î 4 ĵ 3kˆ2 T eists thoughout the egion. () Clculte the mgnetic flu though the shded fce. (b) Wht is the totl flu though the si fces? Figue Conside the hemispheicl closed sufce in Figue The hemisphee is in unifom mgnetic field tht mkes n ngle u with the veticl. Clculte the mgnetic flu though () the flt sufce S 1 nd (b) the hemispheicl sufce S 2. S 1 S 2 u Figue A solenoid 2.50 cm in dimete nd 30.0 cm long hs 300 tuns nd cies 12.0 A. () Clculte the flu though the sufce of disk of dius 5.00 cm tht is positioned pependicul to nd centeed on the is of the solenoid, s shown in Figue (b) Figue 30.41b shows n enlged end view of the sme solenoid. Clculte the flu though the blue e, which is n nnulus with n inne dius of cm nd n oute dius of cm. B B () Figue cm 42. Compe this poblem with oblem 65 in Chpte 24. Conside mgnetic field tht is unifom in diection thoughout cetin volume. Cn it be unifom in mgnitude? Must it be unifom in mgnitude? Give evidence fo ou nswes. Section 30.6 Mgnetism in Mtte 43. At stution, when nel ll the toms hve thei mgnetic moments ligned, the mgnetic field in smple of ion cn be 2.00 T. f ech electon contibutes mgnetic moment of A m 2 (one Boh mgneton), how mn electons pe tom contibute to the stuted field of ion? The numbe densit of toms in ion is ppoimtel toms/m 3. Section 30.7 The Mgnetic Field of the Eth 44. A cicul coil of 5 tuns nd dimete of 30.0 cm is oiented in veticl plne with its is pependicul to the hoiontl component of the Eth s mgnetic field. A hoiontl compss plced t the cente of the coil is mde to deflect 45.0 fom mgnetic noth b cuent of A in the coil. () Wht is the hoiontl component of the Eth s mgnetic field? (b) The cuent in the coil is switched off. A dip needle is mgnetic compss mounted so tht it cn otte in veticl noth south plne. At this loction, dip needle mkes n ngle of 13.0 fom the veticl. Wht is the totl mgnitude of the Eth s mgnetic field t this loction? 45. The mgnetic moment of the Eth is ppoimtel A m 2. () mgine tht the plnet mgnetic field wee cused b the complete mgnetition of huge ion deposit. How mn unpied electons would pticipte? (b) At two unpied electons pe ion tom, how mn kilogms of ion would compose the deposit? on hs densit of kg/m 3 nd ppoimtel ion toms/m A pticul loction on the Eth s sufce is chcteied b vlue of gvittionl field, vlue of mgnetic field, nd vlue of tmospheic pessue. () Which of these quntities e vectos nd which e scls? (b) Detemine vlue fo ech quntit t ou cuent loction. nclude the diection of ech vecto quntit. Stte ou souces. (c) Which of the quntities hve septe cuses fom which of the othes? Additionl oblems 47. A ve long, thin stip of metl of width w cies cuent long its length s shown in Figue Find the mgnetic field t the point in the digm. The point is in the plne of the stip t distnce b w fom it. (b) 2 = intemedite; 3 = chllenging; = SSM/SG; = ThomsonNOW; = smbolic esoning; = qulittive esoning

7 864 Chpte 30 Souces of the Mgnetic Field w tnce pt. Ech coil cies sted cuent in the sme diection s shown in Figue () Show tht the mgnetic field on the is t distnce fom the cente of one coil is b B Nm c > d 3>2 Figue The mgnitude of the Eth s mgnetic field t eithe pole is ppoimtel T. Suppose the field fdes w, befoe its net evesl. Scouts, silos, nd consevtive politicins ound the wold join togethe in pogm to eplce the field. One pln is to use cuent loop ound the equto, without eling on mgnetition of n mteils inside the Eth. Detemine the cuent tht would genete such field if this pln wee cied out. Tke the dius of the Eth s E m. 49. A thin coppe b of length 10.0 cm is suppoted hoiontll b two (nonmgnetic) contcts. The b cies cuent A in the diection s shown in Figue At distnce h cm below one end of the b, long, stight wie cies cuent A in the diection. Detemine the mgnetic foce eeted on the b. 1 h Figue Suppose ou instll compss on the cente of the dshbod of c. Compute n ode-of-mgnitude estimte fo the mgnetic field t this loction poduced b the cuent when ou switch on the hedlights. How does this estimte compe with the Eth s mgnetic field? You m suppose the dshbod is mde mostl of plstic. 51. A nonconducting ing of dius 10.0 cm is unifoml chged with totl positive chge 10.0 mc. The ing ottes t constnt ngul speed 20.0 d/s bout n is though its cente, pependicul to the plne of the ing. Wht is the mgnitude of the mgnetic field on the is of the ing 5.00 cm fom its cente? 52. A nonconducting ing of dius is unifoml chged with totl positive chge q. The ing ottes t constnt ngul speed v bout n is though its cente, pependicul to the plne of the ing. Wht is the mgnitude of the mgnetic field on the is of the ing distnce /2 fom its cente? 53. Two cicul coils of dius, ech with N tuns, e pependicul to common is. The coil centes e dis- 2 (b) Show tht db/d nd d 2 B/d 2 e both eo t the point midw between the coils. We m then conclude tht the mgnetic field in the egion midw between the coils is unifom. Coils in this configution e clled Helmholt coils. Figue oblems 53 nd Two identicl, flt, cicul coils of wie ech hve 100 tuns nd dius of m. The coils e nged s set of Helmholt coils (see Fig ), pllel nd with seption m. Ech coil cies cuent of 10.0 A. Detemine the mgnitude of the mgnetic field t point on the common is of the coils nd hlfw between them. 55. We hve seen tht long solenoid poduces unifom mgnetic field diected long the is of clindicl egion. To poduce unifom mgnetic field diected pllel to dimete of clindicl egion, howeve, one cn use the sddle coils illustted in Figue The loops e wpped ove somewht flttened tube. Assume the stight sections of wie e ve long. The end view of the tube shows how the windings e pplied. The ovell cuent distibution is the supeposition of two ovelpping, cicul clindes of unifoml distibuted cuent, one towd ou nd one w fom ou. The cuent densit J is the sme fo ech clinde. The position of the is of one clinde is descibed b position vecto eltive to the othe clinde. ove tht the S mgnetic field inside the hollow tube is m 0 J/2 downwd. Suggestion: The use of vecto methods simplifies the clcultion. () Figue You m use the esult of oblem 33 in solving this poblem. A ve lge pllel-plte cpcito cies chge with uni- (b) 2 = intemedite; 3 = chllenging; = SSM/SG; = ThomsonNOW; = smbolic esoning; = qulittive esoning

8 oblems 865 fom chge pe unit e s on the uppe plte nd s on the lowe plte. The pltes e hoiontl nd both move hoiontll with speed v to the ight. () Wht is the mgnetic field between the pltes? (b) Wht is the mgnetic field close to the pltes but outside of the cpcito? (c) Wht is the mgnitude nd diection of the mgnetic foce pe unit e on the uppe plte? (d) At wht etpolted speed v will the mgnetic foce on plte blnce the electic foce on the plte? Clculte this speed numeicll. 57. Two cicul loops e pllel, coil, nd lmost in contct, 1.00 mm pt (Fig ). Ech loop is 10.0 cm in dius. The top loop cies clockwise cuent of 140 A. The bottom loop cies counteclockwise cuent of 140 A. () Clculte the mgnetic foce eeted b the bottom loop on the top loop. (b) Suppose student thinks the fist step in solving pt () is to use Eqution 30.7 to find the mgnetic field ceted b one of the loops. How would ou gue fo o ginst this ide? Suggestion: Think bout how one loop looks to bug peched on the othe loop. (c) The uppe loop hs mss of kg. Clculte its cceletion, ssuming the onl foces cting on it e the foce in pt () nd the gvittionl foce. 140 A 140 A Figue Wht objects epeience foce in n electic field? Chpte 23 gives the nswe: n object with electic chge, sttion o moving, othe thn the chged object tht ceted the field. Wht cetes n electic field? An object with electic chge, sttion o moving, s ou studied in Chpte 23. Wht objects epeience foce in mgnetic field? An electic cuent o moving electic chge, othe thn the cuent o chge tht ceted the field, s discussed in Chpte 29. Wht cetes mgnetic field? An electic cuent, s ou studied in Section 30.1, o moving electic chge, s shown in this poblem. () To undestnd how moving chge cetes mgnetic field, conside pticle with chge q S S moving with velocit v. Define the position vecto ˆ leding fom the pticle to some loction. Show tht the mgnetic field t tht loction is B S m 0 4p q v S ˆ (b) Find the mgnitude of the mgnetic field 1.00 mm to the side of poton moving t m/s. (c) Find the mgnetic foce on second poton t this point, moving with the sme speed in the opposite diection. (d) Find the electic foce on the second poton. 59. The chpte-opening photogph shows il gun. il guns hve been suggested fo lunching pojectiles into spce without chemicl ockets nd fo gound-to-i ntimissile wepons of w. A tbletop model il gun 2 (Fig ) consists of two long, pllel, hoiontl ils 3.50 cm pt, bidged b b BD of mss 3.00 g. The b is oiginll t est t the midpoint of the ils nd is fee to slide without fiction. When the switch is closed, electic cuent is quickl estblished in the cicuit ABCDEA. The ils nd b hve low electic esistnce, nd the cuent is limited to constnt 24.0 A b the powe suppl. () Find the mgnitude of the mgnetic field 1.75 cm fom single ve long, stight wie cing cuent 24.0 A. (b) Find the mgnitude nd diection of the mgnetic field t point C in the digm, the midpoint of the b, immeditel fte the switch is closed. Suggestion: Conside wht conclusions ou cn dw fom the Biot Svt lw. (c) At othe points long the b BD, the field is in the sme diection s t point C, but is lge in mgnitude. Assume the vege effective mgnetic field long BD is five times lge thn the field t C. With this ssumption, find the mgnitude nd diection of the foce on the b. (d) Find the cceletion of the b when it is in motion. (e) Does the b move with constnt cceletion? (f) Find the velocit of the b fte it hs tveled 130 cm to the end of the ils. E A C D Figue Fift tuns of insulted wie cm in dimete e tightl wound to fom flt spil. The spil fills disk suounding cicle of dius 5.00 cm nd etending to dius cm t the oute edge. Assume the wie cies cuent t the cente of its coss section. Appoimte ech tun of wie s cicle. Then loop of cuent eists t dius 5.05 cm, nothe t 5.15 cm, nd so on. Numeicll clculte the mgnetic field t the cente of the coil. 61. An infinitel long, stight wie cing cuent 1 is ptill suounded b loop s shown in Figue The loop hs length L nd dius, nd it cies cuent 2. The is of the loop coincides with the wie. Clculte the foce eeted on the loop. L 1 2 Figue The mgnitude of the foce on mgnetic dipole M S ligned with nonunifom mgnetic field in the diection is F 0M S 0 db/d. Suppose two flt loops of wie ech hve dius nd c cuent. () The loops e nged coill nd septed b vible distnce, lge comped with. Show tht the mgnetic foce B 2 = intemedite; 3 = chllenging; = SSM/SG; = ThomsonNOW; = smbolic esoning; = qulittive esoning

9 866 Chpte 30 Souces of the Mgnetic Field between them vies s 1/ 4. (b) Evlute the mgnitude of this foce, tking 10.0 A, cm, nd 5.00 cm. 63. A wie is fomed into the shpe of sque of edge length L (Fig ). Show tht when the cuent in the loop is, the mgnetic field t point, distnce fom the cente of the sque long its is is m 0 L 2 B 2p 1 2 L 2 > L 2 >2 L dil line nd its tngent line t n point on the cuve f(u) is elted to the function s follows: Theefoe, in this cse e u, tn b 1, nd b p/4, nd the ngle between d S s nd ˆ is p b 3p/4. Also, ds tn b d>du d 22 d sin 1p> A sphee of dius hs unifom volume chge densit. Detemine the mgnetic field t the cente of the sphee when it ottes s igid object with ngul speed v bout n is though its cente (Fig ). v L Figue A wie cing cuent is bent into the shpe of n eponentil spil, e u, fom u 0 to u 2p s suggested in Figue To complete loop, the ends of the spil e connected b stight wie long the is. Find the mgnitude nd diection of B S t the oigin. Suggestions: Use the Biot Svt lw. The ngle b between = e u u ˆ Figue d ds b= p/4 Figue oblems 65 nd A sphee of dius hs unifom volume chge densit. Detemine the mgnetic dipole moment of the sphee when it ottes s igid bod with ngul speed v bout n is though its cente (Fig ). 67. A long, clindicl conducto of dius hs two clindicl cvities of dimete though its entie length s shown in Figue A cuent is diected out of the pge nd is unifom though coss section of the conducto. Find the mgnitude nd diection of the mgnetic field in tems of m 0,,, nd t () point 1 nd (b) point 2. 1 Figue Answes to Quick Quies 30.1 B, C, A. oint B is closest to the cuent element. oint C is fthe w, nd the field is futhe educed b the sin u fcto in the coss poduct d S s ˆ. The field t A is eo becuse u (). The coils ct like wies cing pllel cuents in the sme diection nd hence ttct one nothe b, d,, c. Eqution indictes tht the vlue of the line integl depends onl on the net cuent though ech closed pth. th b encloses 1 A, pth d encloses 3 A, pth encloses 4 A, nd pth c encloses 6 A b, then c d. ths, c, nd d ll give the sme noneo vlue m 0 becuse the sie nd shpe of the pths do not mtte. th b does not enclose the cuent; hence, its line integl is eo (c). The mgnetic field in ve long solenoid is independent of its length o dius. Ovewpping with n dditionl le of wie inceses the numbe of tuns pe unit length. 2 = intemedite; 3 = chllenging; = SSM/SG; = ThomsonNOW; = smbolic esoning; = qulittive esoning